We analyze the structure of the Witt group W of braided fusion categories
introduced in the previous paper arXiv:1009.2117v2. We define a "super" version
of the categorical Witt group, namely, the group sW of slightly degenerate
braided fusion categories. We prove that sW is a direct sum of the classical
part, an elementary Abelian 2-group, and a free Abelian group. Furthermore, we
show that the kernel of the canonical homomorphism S: W --> sW is generated by
Ising categories and is isomorphic to Z/16Z. Finally, we give a complete
description of etale algebras in tensor products of braided fusion categories.